Haven't looked at the Mark III adjustable sights, but if they're the same as the tin-like construction of the the old Belgian Browning adjustables, they're surely worth replacing. The don't hold a zero well as Mr. Camp pointed out and they simply scare me because they look fragile tho, I've never given them a chance to shoot loose.
Check the number of used adjustable sight Brownings with missing screws though--they must shoot loose more than any other piece extant (or have the clumsiest screw-losing owners).
For a carrying pistol, the 9mm's are among the few pieces where I prefer adjustable sights since when bouncing about at any given time ammo availability may vary so in bullet wt, velocity, and POI. Because of that, personally, I've opted for the adjustable sight Belgian models since I like the high foresight which comes with them and it minimizes aftermarket modifications that require gunsmith services.
An inexpensive, readily available adjustable sight is the MILLETT which has served me well in the several Hi-Pwrs I've owned and on those of several friends and acquaintances.
The MILLETT is a high riding sight though and not as clean looking as having a low mounted BO-MAR put on and as Mr. Camp points out, nothing is lower riding than having a S&W K-38 sight inlet into the slide. The latter should have a first rate gunsmith install it though. As further support for Mr. Camp's cmts on needing a heavier screw to secure the S&W sight, on my Swenson-Colt 45's, old Armand pinned the sights as well as fitting heavier duty screws to secure tge sights since 45 ball and heavier loads did tend to shoot them loose (and did so on my first piece).